How long would we expect to wait An orderofmagnitude calculation

The minimum energy required to pull an electron out of the metal is of the order of 3 eV. (The electron volt, eV, is the unit of energy commonly used in atomic physics, equal to the energy of an electron which has been accelerated through a potential difference of 1 volt, and is equivalent to 1.60 x 10-19 J.) Let us assume that there is one free electron per atom and that the photoelectron comes from one of the ten layers of sodium atoms closest to the surface. Assuming a light beam is spread out evenly and smoothly with an intensity of 5 x 10-6 Wm-2, we can estimate the time required for an electron to receive the necessary energy as follows:

Estimating the time taken if the light energy is evenly divided

A monolayer of sodium atoms contains ~ 1019 atoms m-2

^ ~ 1020 atoms in 10 layers

5 x 10-6 Wm-2 divided among 1020 atoms = 5 x 10-26 W per atom

Required to liberate electron 3 eV = 3 x 1.6 x 10-19 J

Allowing for the very approximate nature of the above estimate, it is clear that the observed emission of photoelectrons is too fast by at least 16 orders of magnitude. The situation can be compared to the power of the sea which gradually erodes the shore. The energy of the waves is distributed over a large area, and over a long period of time. If this power were concentrated in quanta

of analogous propor- H^s»/ 'vwv tions, we might find the

Rock of Gibraltar ejected suddenly and without warning. 13.1.5 The 'lucky' electron

A model consistent with experimental evidence of the ejection of electrons from a metallic surface by photons is as follows: the atoms of the metal have one or two outer electrons which are relatively 'free' and can be considered as constituting an electron gas within the solid material. These are candidates for ejection not only from the atom but from the surface of the metal. We will assume that the photon collides with an individual electron and gives it enough energy to overcome the potential barrier and escape. Only a tiny fraction of the available electrons is released in the whole process, and which electrons are hit by the photon is entirely a matter of chance. The 'lucky' (or, perhaps, unfortunate) electron receives a whole quantum of energy while its neighbours remain undisturbed.

Some of the liberated electrons are attracted back into the metal, while more escape. In this way a steady state of

Photon bombardment

Surfac of met;

Photon bombardment

Surfac of met;

Photons eject just a tiny fraction of the free electrons

Liberated electrons form an 'electron cloud

Figure 13.1 'Electron gas'.

Photons eject just a tiny fraction of the free electrons

Liberated electrons form an 'electron cloud

Figure 13.1 'Electron gas'.

equilibrium is established with an 'electron cloud' near the surface. The electrons move randomly within the cloud (Figure 13.1).